# How do you solve -27= \frac { 3v - 6} { 8} - \frac { 8v + 9} { 2}?

Aug 1, 2018

See a solution process below:

#### Explanation:

First, multiply each side of the equation by the appropriate form of $1$ to eliminate the fractions while keeping the equation balanced:

$\textcolor{red}{16} \times - 27 = \textcolor{red}{16} \left(\frac{3 v - 6}{8} - \frac{8 v + 9}{2}\right)$

$- 432 = \left(\textcolor{red}{16} \times \frac{3 v - 6}{8}\right) - \left(\textcolor{red}{16} \times \frac{8 v + 9}{2}\right)$

$- 432 = \left(\cancel{\textcolor{red}{16}} \textcolor{red}{2} \times \frac{3 v - 6}{\textcolor{red}{\cancel{\textcolor{b l a c k}{8}}}}\right) - \left(\cancel{\textcolor{red}{16}} \textcolor{red}{8} \times \frac{8 v + 9}{\textcolor{red}{\cancel{\textcolor{b l a c k}{2}}}}\right)$

$- 432 = \textcolor{red}{2} \left(3 v - 6\right) - \textcolor{red}{8} \left(8 v + 9\right)$

$- 432 = \left(\textcolor{red}{2} \times 3 v\right) - \left(\textcolor{red}{2} \times 6\right) - \left(\textcolor{red}{8} \times 8 v\right) + \left(\textcolor{red}{8} \times 9\right)$

$- 432 = 6 v - 12 - 64 v - 72$

Next, group and combine like terms on the right side of the equation:

$- 432 = 6 v - 64 v - 12 - 72$

$- 432 = \left(6 - 64\right) v + \left(- 12 - 72\right)$

$- 432 = - 58 v + \left(- 84\right)$

$- 432 = - 58 v - 84$

Then, add $\textcolor{red}{84}$ to each side of the equation to isolate the $v$ term while keeping the equation balanced:

$- 432 + \textcolor{red}{84} = - 58 v - 84 + \textcolor{red}{84}$

$- 348 = - 58 v - 0$

$- 348 = - 58 v$

Now, divide each side of the equation by $\textcolor{red}{- 58}$ to solve for $v$ while keeping the equation balanced:

$\frac{- 348}{\textcolor{red}{- 58}} = \frac{- 58 v}{\textcolor{red}{- 58}}$

$6 = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 58}}} v}{\cancel{\textcolor{red}{- 58}}}$

$6 = v$

$v = 6$

Aug 1, 2018

$v = 6$

#### Explanation:

$\frac{3 v - 6}{8} - \frac{8 v + 9}{2} = - 27$

$\frac{3 v - 6 - 32 v - 36}{8} = - 27$

$\frac{- 29 v - 42}{8} = - 27$

$- 29 v - 42 = - 216$

$- 29 v = - 174$

$v = \frac{- 174}{- 29} = 6$

Aug 1, 2018

Multiply throughout by 8

$- 216 = \left(3 v - 6\right) - 4 \left(8 v + 9\right)$

Remove the brackets

$- 216 = 3 v - 6 - 32 v - 36$

Collect like terms

$- 216 = - 29 v - 42$

Add $29 v \mathmr{and} 216$ to both sides

$29 v = 174$

Divide by 29

$v = \frac{174}{29}$

$v = 6$